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2.4: Radius of Gyration

Last updated

Mar 5, 2022
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- 2.3: Moments of Inertia of Some Simple Shapes
- 2.5: Plane Laminas and Mass Points distributed in a Plane

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The second moment of inertia of any body can be written in the form $mk^2$ . Thus, for the rod, the disc (about an axis perpendicular to its plane), the triangle and the disc (about a diameter), $k$ has the values

$\dfrac{l}{\sqrt{3}} = 0.866l$ ,
$\dfrac{a}{\sqrt{2}} = 0.707a$ ,
$\dfrac{a}{\sqrt{6}} = 0.408a$ , and
$\dfrac{a}{2} = 0.500a$

respectively.

$k$ is called the radius of gyration. If you were to concentrate all the mass of a body at its radius of gyration, its moment of inertia would remain the same.

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